I remember your lecture from GAME2020 about how GA for physics is not only unifying, but it also brought new ways of thinking about it. Could you elaborate?
I think GA gives you a different approach to various areas in physics. For example, in quantum mechanics GA gives you the ability to model processes right through. For what people think of as the collapse of the wave function, in GA you can see that there is a continuous deterministic evolution, which can still be entirely compatible with the predictions of quantum mechanics, but it gives you a different picture. This is more of a dramatic example, but I think in quite general terms when you get a new bit of complex mathematics, looking at it with GA might simplify things. That is quite helpful, it gives you the bravery to actually tackle much more complicated things.
I recall from your talk (GAME2023) that you propose a 64-dimensional space, based upon the space time algebra, which is just the algebra of 4-D space. Two things about that: There are at the moment 61 particles known, could that imply that there might be three more to discover?
Yes, that would be one of the consequences I think, there could be just a few more particles which are being predicted by the GA approach.
There was another physicist some time ago using an 8×8 complex matrix…
…They believed they got a representation of the standard model within the 64-dimensional space of 8×8 complex matrices, but it is virtually impossible to decode it in order to figure out the geometry underlying it. And so using GA, the geometry becomes clear.
How frustrating is it that you have to translate your findings in GA, in which they are obvious, down to the conventional expressions?
I find that one of the hardest parts, particularly in relativity and general relativity, because I find the conventional calculus approach really tedious and conceptually quite difficult in certain places. Whereas the GA approach is much simpler. On the other hand, when we discover something in the GA approach and we want it to get read by a wide variety of people in astronomy and cosmology, we have to try and translate it, which can be one of the hardest parts.
To what extent is it inevitable for physicists to start to adopt GA, space time algebra, like it should be?
Different people are very good at different things and so there might be some people who will be able to understand things intuitively using the matrix representations. There will always be some amazing people who can look through these deficiencies of whatever mathematical systems they are using, but I think more people will be able to understand these complex things by using GA.